Reopening an H1B 8 years later?

Having an advanced degree I obtained an H1B in October 1998 which I worked on (for 3 different companies via transfers) and ended employment 6 years later in September 2004. I am currently looking for work in the US and a consulting company informed me that once I found employment they could “reopen” the original H1B, and in essence I would not need to apply for a brand new visa, which I am thinking would mean that the current visa cap would not affect me. Is this correct information and can this be done?

As far as I know, an approved cap has only 6 years validity during which time the beneficiary can file a cap-exempt petition. Your H1B was approved 14 years back and hence you wouldn’t be eligible to file a cap-exempt petition now.

Your options are 1) wait till April 2013 to file a cap-subject petition for FY2014 quota and start working from 1st October 2013, or 2) identify a cap-exempt employer, like NFP organization or higher education institution, and file cap-exempt petition and start working as soon as its approved.

Thanks much.